Dr Tewari has developed computational resources with an expansible object-oriented framework in Java for handling exact coalescent recursions and doing Monte Carlo simulations with importance sampling. We have advanced our combinatorial understanding of coalescent results, resulting in concrete improvements to coalescent algorithms. In particular, for importance sampling of coalescent probabilities, Drs. Tewari and Spouge have applied exact probability calculations within the framework to increase the effective sample size by about four with negligible costs in computation time. Dr. Spouge has also developed some coalescent results relevant to inferring events at the initiation of viral infection, e.g., with HIV. As a byproduct of this research, a collaboration with Drs da Silva and Harris developed a new statistical method of analyzing genomes of malaria parasites, resulting in some novel published conclusions about the speciation of malaria. In particular, the results suggest that historically, malaria infection has not jumped species barriers.